Implement linearized version of baseband phase-locked loop

Components sublibrary of Synchronization

The Linearized Baseband PLL block is a feedback control system
that automatically adjusts the phase of a locally generated signal
to match the phase of an input signal. Unlike the Phase-Locked
Loop block, this block uses a baseband model method. Unlike
the Baseband PLL block, which uses
a nonlinear model, this block simplifies the computations by using *x* to
approximate sin(*x*). The baseband PLL model depends
on the amplitude of the incoming signal but does not depend on a carrier
frequency.

This PLL has these three components:

An integrator used as a phase detector.

A filter. You specify the filter's transfer function using the

**Lowpass filter numerator**and**Lowpass filter denominator**parameters. Each is a vector that gives the respective polynomial's coefficients in order of descending powers of*s*.To design a filter, you can use functions such as

`butter`

,`cheby1`

, and`cheby2`

in Signal Processing Toolbox™ software. The default filter is a Chebyshev type II filter whose transfer function arises from the command below.`[num, den] = cheby2(3,40,100,'s')`

A voltage-controlled oscillator (VCO). You specify the sensitivity of the VCO signal to its input using the

**VCO input sensitivity**parameter. This parameter, measured in Hertz per volt, is a scale factor that determines how much the VCO shifts from its quiescent frequency.

This block accepts a sample-based scalar input signal. The input signal represents the received signal. The three output ports produce:

The output of the filter

The output of the phase detector

The output of the VCO

**Lowpass filter numerator**The numerator of the lowpass filter transfer function, represented as a vector that lists the coefficients in order of descending powers of

*s*.**Lowpass filter denominator**The denominator of the lowpass filter transfer function, represented as a vector that lists the coefficients in order of descending powers of

*s*.**VCO input sensitivity (Hz/V)**This value scales the input to the VCO and, consequently, the shift from the VCO's quiescent frequency.

For more information about phase-locked loops, see the works
listed in Selected Bibliography for Synchronization in *Communications System Toolbox™ User's
Guide*.

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